Accurately estimating the mixed oil length plays a big role in the economic benefit for oil pipeline network. While various proposed methods have tried to predict the mixed oil length, they often exhibit an extremely high probability (around 50\%) of underestimating it. This is attributed to their failure to consider the statistical variability inherent in the estimated length of mixed oil. To address such issues, we propose to use the conditional diffusion model to learn the distribution of the mixed oil length given pipeline features. Subsequently, we design a confidence interval estimation for the length of the mixed oil based on the pseudo-samples generated by the learned diffusion model. To our knowledge, we are the first to present an estimation scheme for confidence interval of the oil-mixing length that considers statistical variability, thereby reducing the possibility of underestimating it. When employing the upper bound of the interval as a reference for excluding the mixed oil, the probability of underestimation can be as minimal as 5\%, a substantial reduction compared to 50\%. Furthermore, utilizing the mean of the generated pseudo samples as the estimator for the mixed oil length enhances prediction accuracy by at least 10\% compared to commonly used methods.

翻译：准确估计混油长度对输油管网的经济效益具有重要作用。尽管已有多种方法尝试预测混油长度，但这些方法往往存在极高的低估概率（约50%）。这归因于它们未能考虑混油长度估计中固有的统计变异性。为解决此问题，我们提出使用条件扩散模型来学习给定管道特征下混油长度的分布。随后，我们基于学习到的扩散模型生成的伪样本，设计了混油长度的置信区间估计方法。据我们所知，我们首次提出了考虑统计变异性的混油长度置信区间估计方案，从而降低了低估的可能性。当使用区间上界作为混油排除的参考标准时，低估概率可降至最低5%，较原有的50%大幅降低。此外，使用生成的伪样本均值作为混油长度的估计量，与常用方法相比，预测精度至少提高了10%。